Generation of modulated magnetic structure based on cluster multipole: Application to $\alpha$-Mn and Co$M_3$S$_6$

TL;DR

This paper introduces a systematic method to generate symmetry-adapted magnetic structures with propagation vector k, enabling analysis of complex modulated magnetic structures and identifying those inducing anomalous Hall effects.

Contribution

The method extends multipole expansion techniques to include arbitrary propagation vectors, allowing comprehensive derivation of magnetic structures compatible with crystal symmetry.

Findings

Applied to $ ext{α}$-Mn and Co$M_3$S$_6$, revealing magnetic structures responsible for anomalous Hall effects.

Identified magnetic configurations that induce Hall effects without net magnetization.

Provided a framework for analyzing emergent multipoles in complex magnetic phases.

Abstract

We present a systematic method to automatically generate symmetry-adapted magnetic structures for given crystal structure and general propagation vector k as an efficient approach of the analysis of complex modulated magnetic structures. The method is developed as an extension of the generation scheme based on multipole expansion, which was demonstrated only for the propagation vector k=0 [M.-T. Suzuki et al., Phys. Rev. B 99, 174407 (2019)]. The symmetry-adapted magnetic structures characterized with an ordering vector k are obtained by mapping the multipole magnetic alignments on a virtual cluster to the periodic crystal structure with the phase factor for the wave vector k. This method provides all magnetic bases compatible with irreducible representations under k-group for given crystal structure and wave vector k. Multiple-k magnetic structures are derived from superposition of single-k magnetic bases related with space group symmetry. We apply the scheme to deduce the magnetic structures of $\alpha$-Mn and Co$M_{3}$S$_6$ (M = Nb, Ta), in which large anomalous Hall effect has recently been observed in antiferromagnetic phases, and identify the magnetic structures inducing anomalous Hall effect without net magnetization. The physical phenomena originating from emergent multipoles in the ordered phases are also discussed based on the Landau theory.